Abstract
<jats:p>This article explores the theoretical foundations and mathematical characteristics of systems of parametric trigonometric equations, as well as their application in various scientific and technical domains. The paper presents the core principles of modeling physical phenomena—such as pendulum oscillations, rotational motion, alternating current in electrical engineering, and wave processes— using systems of parametric trigonometric equations. It also examines the key properties of these solutions, including periodicity, amplitude, and phase, emphasizing their significance for accurately and thoroughly describing the dynamics of real-world systems. In the practical section, the use of parametric trigonometric equations is demonstrated through examples involving rotational motion, harmonic oscillations, and the analysis of electrical signals. Graphs and calculations are used to show that these equations are effective tools for modeling dynamic processes. The findings of the study suggest that the presented approaches can be widely applied in scientific research and engineering practice.</jats:p>